Searches for a better (more parsimonious) tree by swapping subtrees which are separated by many edges.
Instead the K.L. optimizer selects several "paths" through the tree (we call this selection 'path reduction') and follows only those paths, while performing NNIs (see ´NNI (Nearest Neighbour Interchange)´) along it's way.
These NNIs are even attempted, when single NNIs degrade the quality of the topology. If some intermediate or the final NNI (which is by default done 15 edges away from the edge starting from) leads to an improvement of the tree, the topology change is kept. Otherwise all changes are undone and the next path will be attempted.